Dear BKH33AL,
Thanks for choosing Microsoft community!
I have read your question carefully and done some research, please kindly refer to following suggestions:
I suggest you log into your account with your browser (put Outlook into work off line) and clean up your folders. You might be better off delete Exchange account so it deletes the cache files in Outlook then add account back after you have cleaned up.
Exchange Basics: The Inbox syncs more frequently than any other and should be kept as clean as possible. (this is the number one cause of problems with sync). Do not make subfolders under the Inbox. Any folder with more than a few thousand messages is going to take some time to fully come down when you first sync your account. Due to the design of Outlook's sync engine (and how exchange works), you will see the 512 newest messages in a folder at the initial start of sync then the rest of the folder's contents will be back filled before you see any mail that arrives after this point. This is why it will look like you are not getting new mail when a folder is still going through initial sync. This is also further exacerbated by an Exchange issue where it gets unnecessary change events before the newer mail arrives. If you carefully watch the progress during the sync of a folder with greater than a couple thousand messages, you will see "Updating local..." a lot before the newer mail starts arriving. Outlook checks the server for updates every minute, any folder that has updates will subsequently be synced. Since Outlook has a limit on how many folders can be synced at a time, there can be a queue of folders waiting. The Inbox does get high priority so it will generally sync before other folders that also need to sync.
If problem persists, to save your time and help you better, please try to connect outlook for Mac support. There will be a professional outlook for Mac technician there to help you. Please refer to this article: Contact support within Outlook for Mac (microsoft.com)
Hope this help you, if there is any deviation in my understanding, please forgive me and provide me with more details. I am more than happy to continue to help you. I wish you a smooth new year and all the best!
Best regards,
Kerry